A Thermal–Hydraulic–Mechanical–Chemical Coupling Model for Acid Fracture Propagation Based on a Phase-Field Method

authored by: Yifan Dai, Bing Hou, Sanghyun Lee, Thomas Wick
Abstract: Acid fracturing is a technique to enhance productivity in carbonate formations. In this work, a thermal–hydraulic–mechanical–chemical (THMC) coupling model for acid fracture propagation is proposed based on a phase-field approach. The phase-field variable is utilized as an indicator function to distinguish the fracture and the reservoir, and to track the propagation of the fracture. The resulting system is a nonstationary, nonlinear, variational inequality system in which five different physical modules for the displacement, the phase-field, the pressure, the temperature, and the acid concentration are coupled. This multi-physical system includes numerical challenges in terms of nonlinearities, solution coupling algorithms, and computational cost. To this end, high fidelity physics-based discretizations, parallel solvers, and mesh adaptivity techniques are required. The model solves the phase-field and the displacement variables by a quasi-monolithic scheme and the other variables by a partitioned schemes, where the resulting overall algorithm is of iterative coupling type. In order to maintain the computational cost low, the adaptive mesh refinement technique in terms of a predictor-corrector method is employed. The error indicators are obtained from both the phase-field and concentration approximations. The proposed model and the computational robustness were investigated by studying fourteen cases as well as some mesh refinement studies. It is observed that the acid and thermal effect increase the fracture volume and fracture width. Moreover, the natural fractures and holes affect the acid fracture propagation direction.
Organisation(s): Institute of Applied Mathematics
External Organisation(s): China Univeristy of Petroleum - Beijing
Florida State University
Type: Article
Journal: Rock Mechanics and Rock Engineering
ISSN: 0723-2632
Publication date: 01.03.2024
Publication status: E-pub ahead of print
Peer reviewed: Yes
ASJC Scopus subject areas: Civil and Structural Engineering, Geotechnical Engineering and Engineering Geology, Geology
Electronic version(s): https://doi.org/10.1007/s00603-024-03769-x (Access: Closed)

BibTeX

@article{c3eadebeb6744e3b94fbf221adce1746,
title = "A Thermal–Hydraulic–Mechanical–Chemical Coupling Model for Acid Fracture Propagation Based on a Phase-Field Method",
abstract = "Acid fracturing is a technique to enhance productivity in carbonate formations. In this work, a thermal–hydraulic–mechanical–chemical (THMC) coupling model for acid fracture propagation is proposed based on a phase-field approach. The phase-field variable is utilized as an indicator function to distinguish the fracture and the reservoir, and to track the propagation of the fracture. The resulting system is a nonstationary, nonlinear, variational inequality system in which five different physical modules for the displacement, the phase-field, the pressure, the temperature, and the acid concentration are coupled. This multi-physical system includes numerical challenges in terms of nonlinearities, solution coupling algorithms, and computational cost. To this end, high fidelity physics-based discretizations, parallel solvers, and mesh adaptivity techniques are required. The model solves the phase-field and the displacement variables by a quasi-monolithic scheme and the other variables by a partitioned schemes, where the resulting overall algorithm is of iterative coupling type. In order to maintain the computational cost low, the adaptive mesh refinement technique in terms of a predictor-corrector method is employed. The error indicators are obtained from both the phase-field and concentration approximations. The proposed model and the computational robustness were investigated by studying fourteen cases as well as some mesh refinement studies. It is observed that the acid and thermal effect increase the fracture volume and fracture width. Moreover, the natural fractures and holes affect the acid fracture propagation direction.",
keywords = "Acid fracture propagation, Adaptive finite elements, Multiphysics, Phase-field method, Predictor–corrector mesh refinement",
author = "Yifan Dai and Bing Hou and Sanghyun Lee and Thomas Wick",
note = "Funding Information: The authors are grateful to The National Key Research and Development Program of China under Grant (NO. 2022YFE0129800) and The National Natural Science Foundation of China (No. 52074311 and No.U19B6003-05). The first author is supported by a CSC scholarship. Moreover, the first author gratefully acknowledges the hospitality and computing resources at the Institute of Applied Mathematics during his CSC research stay. Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature 2024.",
year = "2024",
month = mar,
day = "1",
doi = "10.1007/s00603-024-03769-x",
language = "English",
journal = "Rock Mechanics and Rock Engineering",
issn = "0723-2632",
publisher = "Springer-Verlag Wien",
}